Linking stand productivity with stand structure

Stand structure can strongly influence forest growth and other processes, such as the water balance, carbon partitioning, nutrient cycling and light dynamics. However, individual structural variables can be positively or negatively correlated with growth. This is the case for variables such as size inequality and those that describe resource partitioning, such as the degree of symmetric/asymmetric competition and growth dominance. In these projects, several contrasting growth-structure correlations were examined and linked to forest processes by considering the different types of tree interactions they are associated with.

Contrasting growth-structure correlations appear to converge when they are examined using a simple framework where stand growth is a function of three variables as opposed to any one of the variables alone; stand density, size distributions and size-growth relationships (1, Figure 1), such that:

Stand growth = stand density x size probability density function x size-growth relationship (Eq. 1)

The size distributions quantify how the stand density is distributed between the different sizes while the size-growth relationships quantify how growth is partitioned between different sizes. Size inequality may not often be a useful explanatory variable and instead it appears to sometimes correlate with growth because it can be correlated with other variables that influence growth (1).

Figure 1. An illustration of Equation 1. The frequency distributions are the red curves in the left panels. These are the products of the stand density and the probability density functions of Equation 1. The individual tree size-growth relationships are blue curves in the upper panels. All other panels (with black curves) are the result of the given frequency distribution ´ size-growth relationship, and indicate the resulting stand basal area growth (Gr; m² ha^-1 year^-1) and the growth dominance coefficient (DC_growth) with its associated dominance curve (solid black line). The black dashed lines are 1:1 lines. The frequency distribution and size-growth relationships are in terms of individual tree basal area (cm²) and basal area growth (cm² year^-1). All stands have a stand density of 40 m² ha^-1. This graph is based on growth but it could be based on processes like transpiration, light absorption, drought stress etc. While some of the size-growth shapes are unlikely, they are included to facilitate the illustration of the contrasting shapes. For simplicity, no complex size distributions are shown (e.g. bi-modal). Figure from (1).

The spatial and temporal dynamics of the effects of structure on growth have received little attention and a long-term growth and yield data set from central Europe was used to examine how the effects of structure can change along climatic gradients. The simple framework of three variables could be used to separate the effects of structure and functioning when comparing mixed and monospecific forests, as well as to design silvicultural interventions or to determine whether past management interventions have achieved their goals. The main review paper from this project also discussed some of the implications for selecting which structural variables to use and when scaling up to the stand level.

The framework illustrated in Figure 1 helps to explain why stands with bell-shaped distributions, such as those on the left, can differ in productivity to the stands with reverse-J shaped distributions (on the right), even though the species compositions and stand densities might be the same. The top photos are of Fagus sylvatica forests, while the bottom photos are of mixed Picea abies and Abies alba forests in Switzerland. The photos on the left are from even-aged forests, while those on the right are uneven-aged (or all-aged) forests.

Journal articles related to this project:

1. Forrester, D.I., 2019. Linking forest growth with stand structure: Tree size inequality, tree growth or resource partitioning and the asymmetry of competition. Forest Ecology and Management 447, 139-157. doi:10.1016/j.foreco.2019.05.053

2. Forrester, D.I., Ammer, C., Annighöfer, P.J., Barbeito, I., Bielak, K., Bravo-Oviedo, A., Coll, L., Río, M.d., Drössler, L., Heym, M., Hurt, V., Löf, M., Ouden, J.d., Pach, M., Pereira, M.G., Plaga, B., Ponette, Q., Skrzyszewski, J., Sterba, H., Svoboda, M., Zlatanov, T., Pretzsch, H. (2018). Effects of crown architecture and stand structure on light absorption in mixed and monospecific Fagus sylvatica and Pinus sylvestris forests along a productivity and climate gradient through Europe. Journal of Ecology. 106, 746-760. doi:10.1111/1365-2745.12803

3. Resende, R.T., Soares, A.A.V., Forrester, D.I., Marcatti, G.E., Santos, A.R.d., Takahashi, E.K., Silva, F.F.e., Grattapaglia, D., Resende, M.D.V., Leite, H.G., (2018). Environmental uniformity, site quality and tree competition interact to determine stand productivity of clonal Eucalyptus. Forest Ecology and Management 410, 76-83. doi:10.1016/j.foreco.2017.12.038

4. Sun, H., Diao, S., Liu, R., Forrester, D., Soares, A., Saito, D., Dong, R., Jiang, J., (2018). Relationship between size inequality and stand productivity is modified by self-thinning, age, site and planting density in Sassafras tzumu plantations in central China. Forest Ecology and Management 422, 199-206. doi: 10.1016/j.foreco.2018.02.003

5. del Río, M., Pretzsch, H., Ruíz-Peinado, R., Ampoorter, E., Annighöfer, P., Barbeito, I., Bielak, K., Brazaitis, G., Coll, L., Drössler, L., Fabrika, M., Forrester, D.I., Heym, M., Hurt, V., Kurylyak, V., Löf, M., Lombardi, F., Madrickiene, E., Matović, B., Mohren, F., Motta, R., den Ouden, J., Pach, M., Ponette, Q., Schütze, G., Skrzyszewski, J., Sramek, V., Sterba, H., Stojanović, D., Svoboda, M., Zlatanov, T. & Bravo-Oviedo, A. (2017). Species interactions increase the temporal stability of community productivity in Pinus sylvestris-Fagus sylvatica mixtures across Europe. Journal of Ecology 105, 1032-1043 doi:10.1111/1365-2745.12727

6. Pretzsch, H., Río, M.d., Schütze, G., Ammer, C., Annighöfer, P., Avdagic, A., Barbeito, I., Bielak, K., Brazaitis, G., Coll, L., Drössler, L., Fabrika, M., Forrester, D.I., Kurylyak, V., Löf, M., Lombardi, F., Matović, B., Mohren, F., Motta, R., Ouden, J.d., Pach, M., Ponette, Q., Skrzyszewski, J., Sramek, V., Sterba, H., Svoboda, M., Verheyen, K., Zlatanov, T., Bravo-Oviedo, A. (2016). Mixing of Scots pine (Pinus sylvestris L.) and European beech (Fagus sylvatica L.) enhances structural heterogeneity, and the effect increases with water availability. Forest Ecology and Management 373, 149-166. doi:10.1016/j.foreco.2016.04.043

7. Soares, A.A.V., Leite, H.G., Souza, A.L., Silva, S.R., Lourenço, H.M., Forrester, D.I. (2016). Increasing stand structural heterogeneity reduces productivity in Brazilian Eucalyptus monoclonal stands. Forest Ecology and Management 373, 26-32. doi:10.1016/j.foreco.2016.04.035

8. Soares, A. A. V., Leite, H. G., Cruz, J. P., Forrester, D. I. (2017). Development of stand structural heterogeneity and growth dominance in thinned Eucalyptus stands in Brazil. Forest Ecology and Management. 384, 339-346. doi:10.1016/j.foreco.2016.11.010

9. Forrester, D.I., Elms, S.R., Baker, T.G. (2013). Tree growth-competition relationships in thinned Eucalyptus plantations vary with stand structure and site quality. European Journal of Forest Research. 132, 241-252. doi:10.1007/s10342-012-0671-0

10. Soares, A.A.V., Scolforo, H.F., Forrester, D.I., Carneiro, R.L., Campoe, O.C., (2020). Exploring the relationship between stand growth, structure and growth dominance in Eucalyptus monoclonal plantations across a continent-wide environmental gradient in Brazil. Forest Ecology and Management 474, 118340. doi:10.1016/j.foreco.2020.118340

11. Torresan, C., Río, M.d., Hilmers, T., Notarangelo, M., Bielak, K., Binder, F., Boncina, A., Bosela, M., Forrester, D.I., Hobi, M., Nagel, T.A., Pach, M., Sitkova, Z., Zlatanov, T., Tognetti, R., Pretzsch, H., (2020) Importance of tree species size dominance and heterogeneity on the productivity of spruce-fir-beech mountain forest stands in Europe. Forest Ecology and Management. 457, 117716. doi:10.1016/j.foreco.2019.117716

12. Brunner, A., Forrester, D.I., (2020). Tree species mixture effects vary with stand density – An analysis based on individual tree responses. Forest Ecology and Management 473, 118334. doi:10.1016/j.foreco.2020.118334

13. Ouyang, S., Xiang, W., Gou, M., Chen, L., Lei, P., Xiao, W., Deng, X., Zeng, L., Li, J., Zhang, T., Peng, C., Forrester, D.I., (2021). Stability in subtropical forests: The role of tree species diversity, stand structure, environmental and socio-economic conditions. Global Ecology and Biogeography. 30, 500-513. doi:10.1111/geb.13235